What is the 32nd term of the arithmetic sequence where a1 = −33 and a9 = −121? −396 −385 −374 −363

The formula to find the general term of an arithmetic sequence is,[tex] a_{n} =a_{1} +(n-1)d [/tex]Where [tex] a_{n} [/tex]= nth term and[tex] a_{1} [/tex] = First term.Given, a9 = −121. Therefore, we can set up an equation as following:[tex] -33+(9-1)d = -121 [/tex] Since, a1 = -33- 33 + 8d = -121 -33 + 8d + 33 = -121 + 33 Add 33 to each sides of the equation.8d = -88.[tex] \frac{8d}{8} =\frac{-88}{8} [/tex] Divide each sides by 8.So, d = - 11.Now to find the 32nd terms, plug in n = 32, a1 = -33 and d = -11 in the above formula. So, [tex] a_{32} = -33 +(32 -1) (-11) [/tex] = -33 + 31 ( -11) = - 33 - 341 = -374So, 32nd term = - 374.Hope this helps you!